Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in JAVA):

Solution:
import java.util.Arrays;
import java.util.Comparator;
import java.util.Scanner;

public class Main {
    static Integer[] l;
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n=sc.nextInt();
        l=new Integer[n];
        for(int i=0;i<n;i++) {
            l[i]=sc.nextInt();
        }
        Arrays.sort(l,Comparator.reverseOrder());
        double max=Math.max(f(2,3,0,1), f(0,3,1,2));
        for(int i=2;i<n-1;i++) {
            max=Math.max(max, f(0,1,i,i+1));
        }
        System.out.printf("%5f",max);
    }
    static double f(int a,int b,int c,int d) {
        return (double)(l[a]+l[b])/(double)(l[c]-l[d]);
    }
}